Stochastic seismic response analysis of soft soil sites

A well-known equivalent linearization technique is proposed for the stochastic response analysis in the time-domain of horizontally layered soil deposits under vertically propagating random shear waves. The Bouc-Wen smooth hysteretic model is used and properly extended to better represent the nonlinear-hysteretic shearing stress-strain relation of soils observed under cyclic loading with fixed and variable limits. The earthquake ground motions are modeled as nonstationary Gaussian processes and the soil response is obtained in terms of its response statistics from which the statistics of the surface ground accelerations and site-specific response spectra can be obtained.     

Status and research needs for prediction of seismic response in liquid containers

Current methods for seismic design of liquid storage tanks and steam suppression pools are reviewed to establish requirements for future research. The use of a transfer function and response spectrum method is emphasized for prediction of slosh response and impulsive loading. The method is also applicable to operating transient loads that occur in nuclear power plants. Direct applicability is noted for much of the available design data that had previously been developed for aerospace launch vehicles.     

Approximate formulas to calculate the seismic response of light attachments to buildings

Simple approximate formulas are proposed to compute the maximum response of equipment or any other light secondary system attached to buildings subjected to earthquake ground motions. The formulas are derived on the basis of a modified version of the conventional response spectrum method and the consideration of building and attachment as one unit. Notwithstanding, they are expressed in terms of the independent dynamic properties of the two components and ordinates from the response spectrum of a specified ground motion. Secondary systems with multiple degrees of freedom attached to one or two arbitrary points of a supporting multistory structure may be considered. As presented, however, the formulas are restricted to cases in which the independent primary and secondary systems are linear elastic with classical modes of vibration, and the masses of the secondary system are small in comparison with those of the primary one. Their accuracy is verified by means of a comparative study with time-history solutions. In this comparative study, the approximate formulas yield an average error of about 4% and a maximum of about 22%.     

Seismic response of tuned single degree of freedom secondary systems

Modal synthesis procedure for evaluating spectral acceleration in the single degree of freedom (SDOF) secondary system oscillator is studied. Problems encountered in the evaluation of response for secondary oscillators that are tuned or nearly tuned with the primary system modes are discussed and solutions to these problems are presented. A new hybrid approach is proposed that gives accurate spectral acceleration in tuned secondary systems for both cases of zero and non zero mass ratio in structures that are nonclassically damped. Formulations are developed to evaluate the interaction-free (zero mass ratio) instructure spectral accelerations for perfectly tuned secondary oscillators in a coupled primary-secondary system when the two uncoupled systems have same damping characteristics (classical damping case).     

Active seismic response control systems for nuclear power plant equipment facilities

To sustain severe earthquake ground motion, a new type of anti-seismic structure is proposed, called a Dynamic Intelligent Building (DIB) system, which is positioned as an active seismic response controlled the structure. The structural concept starts from a new recognition of earthquake ground motion, and the structural natural frequency is actively adjusted to avoid resonant vibration, and similarly the external counter-force cancels the resonant force which comes from the dynamic structural motion energy. These concepts are verified using an analytical simulator program. The advanced application of the DIB system, is the Active Supporting system and the Active Stabilizer system for nuclear power plant equipment facilities.     

Seismic response of multiply connected MDOF primary and MDOF secondary systems

New algorithms are presented to evaluate the mode shapes and frequencies of a coupled system, given the mode shapes and frequencies of the uncoupled primary and secondary systems. These coupled mode shapes can be used to obtain the dynamic response of the total system given the input to the primary system. This information can also be used to develop instructure response spectra (IRS) at the connecting DOF, along with the correlation between the motions at the connecting DOF.     

Stochastic effects when determining the maximum RBMK channel power

The assertion that the system monitoring the distribution of energy release in RBMK systematically overstates the maximum channel power was formulated previously in connection with the problem of increasing reactor power. In the present article, this assertion is analyzed using mathematical modeling which includes the stochastic variation of certain parameters.     

Effective duration of seismic acceleration and occurrence of maximum responses

The maximum response of structures due to a seismic excitation is generally obtained through dynamic analysis, using the entire history of the accelerogram. However, due to the damping effect of structures, only a certain portion of the accelerogram is effective and contributes significantly to the peak response. This paper introduces an efficient procedure for separately 1) selecting the effective duration from a seismic excitation, and 2) predicting the occurrence time of the response maxima.An analytical procedure is developed to determine the effective duration for a seismic excitation, based on the study of the structural responses and the control on error bound. Three multi-degree-of-freedom structures are subjected to several accelerograms, results obtained prove the accuracy of the procedure.The occurrence of the response maxima is derived analytically for the two extreme cases of structural rigidity, namely very flexible (e.g. tall stacks), and very rigid (e.g. power reactors). For structures with intermediate rigidity, the response due to various actual accelerogram indicates the correlation between the response maxima and the arrival frequency of seismic waves.     

Effects of ductility on seismic response of piping systems and their implication on design and qualification

This study is concerned with the inelastic seismic response of nuclear power plant piping systems. Two systems are examined. The first one is an idealized four-equal-span pipe run and the second one consists of two configurations modified from an existing pipe run. Detailed finite element seismic time history analyses are performed using the computer program. By varying the various geometrical and physical parameters, calculations are made for a total of 76 cases. The results show that ductility generally contributes to reducing the response of piping systems. An empirical relation between the support load reduction factor and support ductility demand is given and a chart and simple procedures are suggested for the design and qualification of piping supports taking ductility into consideration.     

Vertical seismic response of overhead crane

Vertical seismic response behavior is an important issue for the seismic design of equipments. The equipment, which is comparatively soft and unrestrained vertically, may resonate and its response is significantly magnified under vertical seismic excitation. Overhead crane is an example of equipment that is unrestrained vertically. The dynamic behavior of an 150-ton-capacity overhead crane under vertical seismic excitation was investigated by scale model excitation test and nonlinear time history analysis. The excitation tests were performed with several input levels and the vertical response with each input level was obtained. The simulation analysis approximately corresponded to the results of the excitation test.     

Two methods for seismic analysis of non-classically damped systems

Two methods of seismic analysis of non-classically damped systems are compared. The first method is an extension of the Foss method (called the modified Foss method here) in which the response in the time domain is represented in terms of real modal vectors and relative displacements and velocities of the equivalent single-degree-of-freedom (SDOF) systems. In the second method, known as the canonical method, a different set of real modal vectors along with sine and cosine responses of the equivalent SDOF systems are used. It is shown that the canonical method can be derived along the same lines as the modified Foss method. The time domain responses from the two methods are identical and the corresponding response spectra responses comparable. The modified Foss method is preferred because of the physical significance of the relative displacements and velocities used in the method.     

A new instructure response spectrum (IRS) method for multiply connected secondary systems with coupling effects

A method of performing coupled response spectrum analysis of secondary systems is presented. The response spectrum specified at the base of the primary system is used as the input. The complex coupled mode shapes along with frequencies and damping values are calculated using an efficient and accurate perturbation scheme. The new method is applied to a 2 DOF secondary system coupled with a 6 DOF secondary system. The masses and the stiffness of the secondary system are varied to get nine different cases. The coupled system is subjected to El Centro (S00E, 1940) ground motion. It is shown that the response values from the present method are in good agreement with those from the coupled time history analysis. The conventional floor response spectrum method gives response values which are consistently much higher than the corresponding values from the time history analysis. It is concluded that the present method is sufficiently straightforward and efficient, and that it yields accurate response values.     

Equivalent modal response method for seismic design of structures

A new method is proposed in which the response in several modes of vibration under the three components of earthquake is replaced by the response in a small number of equivalent modes.     

Analysis of seismic testing motions with instantaneous response spectra

Synthetic multiple-frequency and single-frequency motions are analyzed for their adequacy to simulate a calculated seismic motion for seismic testing of nuclear power plant equipment. The analysis is performed by first comparing their time-independent response spectra and then comparing response spectra derived at an instant of time, that is, instantaneous response spectra. The results show that even though the time-independent response spectrum of the calculated motion is fully enveloped by that of a synthetic test motion, full enveloping is never obtained with the actual responses at any given time. Recommendations are given on practical test methods and type of test motions.     

Dynamic decoupling of multiply connected MDOF secondary systems

The dynamic analysis of primary systems must often be performed decoupled from the secondary system. In doing so, one should assure that the decoupling does not significantly affect the frequencies and the response of the primary systems. The practice consists of heuristic algorithms intended to limit changes in the frequencies. The change in response is not considered. In this paper, changes in both the frequencies and the response are considered. Rational, but simple algorithms are derived to make accurate predictions. Material up to MDOF primary-SDOF secondary system is presented in this paper. MDOF-MDOF systems are treated in a companion paper.     

Preliminary evaluation of the seismic response of the ELSY LFR

The main goal of the present study is the preliminary evaluation of the seismic demand of a LFR with reference to European Lead System project (ELSY) considered one of the most promising innovative Generation IV reactor. The safety aspects of the ELSY reactor in the event of a Safe Shutdown Earthquake, taking into account also the effects of the possible fluid–structure interaction, have been analyzed.To the purpose to determine the seismic demand, in according with the international rules, a non-linear dynamic analysis method was used with rather refined 3-D model of LFR for the foreseen structural analyses and simulations of the plant and of the reactor internals behaviour. In this report numerical results are presented and discussed highlighting the relevance of the fluid–structure interaction in terms of structural integrity as well as the isolation technique effectiveness, which is expected to increase the safety margin of the reactor structures during a seismic event, if the isolators frequency is far from that of the reactor.The present work has been performed within the 6th European Framework Project.     

Evaluation of secondary and higher order response facets in response spectrum analysis

In structural dynamics, designers are concerned not only with primary or first order response facets, i.e. those directly involved in the problem formulation, but also with others which will be generically called higher order facets since they are obtained as linear combination of lower order ones.Direct application of linear combination formulae of lower order facets does not make much sense in the context of Response Spectrum Analysis. In fact, it is usually conservative and anyway unrealistic, the only known thing about the lower order variables being their peak values which are not simultaneous.This paper presents an effective method for treating the results of a Response Spectrum Analysis without adding undesirable conservatism. This method leads to exact peak values of any higher order facets whenever the linear combination coefficients are known a priori. If they are not — as, for example, in the case of obtaining principal stresses — the higher order facet peak value can also be evaluated with enough accuracy.Finally, it permits to find out sets of compatible values of several facets of the same order, affecting the same or different points of the structure, thus enlarging the scope of the Response Spectrum Analysis method which is supposed to provide only maxima regardless of the fact that they usually are not simultaneous. This last capability being of paramount importance when deciding about the structure's capacity to undergo the excitation.     

Improved response factor methods for seismic fragility of reactor building

A seismic probabilistic risk assessment (PRA) method has been applied to evaluate the safety of nuclear reactor buildings during earthquakes. Improvement was made to two methods (based on linear response and based on non-linear response) of fragility analysis in seismic PRA. The conventional method, which is based on linear response, considers increases of seismic capacity implicitly, using the non-linear behaviour of the structure. We described how to evaluate the capacity increase factor for the linear response method. Secondly, we proposed a method based on the non-linear response and a stratified two-point estimation method which can efficiently evaluate the variability of non-linear responses. We applied the two method to a PWR-type nuclear reactor building and ascertained that these method are useful and effective.